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Rewriting Induction + Linear Arithmetic = Decision Procedure

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Automated Reasoning (IJCAR 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7364))

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Abstract

This paper presents new results on the decidability of inductive validity of conjectures. For these results, a class of term rewrite systems (TRSs) with built-in linear integer arithmetic is introduced and it is shown how these TRSs can be used in the context of inductive theorem proving. The proof method developed for inductive theorem proving couples (implicit) inductive reasoning with a decision procedure for the theory of linear integer arithmetic with (free) constructors. The effectiveness of the new decidability results on a large class of conjectures is demonstrated by an evaluation of the prototype implementation Sail2.

This work was supported in part by the “Concept for the Future” of Karlsruhe Institute of Technology within the framework of the German Excellence Initiative and by NSF awards CCF-0729097 and CNS-0905222.

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Author information

Authors and Affiliations

  1. Inst. for Theoretical Computer Science, KIT, Germany

    Stephan Falke

  2. Dept. of Computer Science, University of New Mexico, USA

    Deepak Kapur

Authors
  1. Stephan Falke
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  2. Deepak Kapur
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Editor information

Editors and Affiliations

  1. Fakultät für Informatik, Technische Universität Wien, Favoritenstr. 9, E185/2, 1040, Wien, Austria

    Bernhard Gramlich

  2. École Polytechnique, INRIA Saclay and Laboratoire d’Informatique, Route de Saclay, 91128, Palaiseau Cedex, France

    Dale Miller

  3. School of Computer Science, University of Manchester, Oxford Road, M13 9PL, Manchester, UK

    Uli Sattler

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Falke, S., Kapur, D. (2012). Rewriting Induction + Linear Arithmetic = Decision Procedure. In: Gramlich, B., Miller, D., Sattler, U. (eds) Automated Reasoning. IJCAR 2012. Lecture Notes in Computer Science(), vol 7364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31365-3_20

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  • DOI: https://doi.org/10.1007/978-3-642-31365-3_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31364-6

  • Online ISBN: 978-3-642-31365-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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